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Dominik Benkovič

Bio: Dominik Benkovič is an academic researcher from University of Maribor. The author has contributed to research in topics: Triangular matrix & Algebra representation. The author has an hindex of 11, co-authored 17 publications receiving 463 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the concept of extremal biderivation of a triangular algebra is defined, and it is shown that under certain conditions, under certain assumptions, the extremal and inner biderivities of a triangle algebra can be combined.

81 citations

Journal ArticleDOI
TL;DR: In this article, the authors define an antiderivation from an algebra A into an A -bimodule M as a linear map δ : A → M such that δ(ab) = ǫ(b)aǫ+ǫbǫǫ (a) for all a, b ∈ A.

75 citations

Journal ArticleDOI
TL;DR: The problem of describing the form of a bilinear map B : A × A → A satisfying B ( x, x ) x = x B (x, x ) for all x ∈ A is considered in this paper, where commutativity preserving maps and Lie isomorphisms of certain triangular algebras are determined.

75 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduced the notion of multiplicative Lie n-derivation of a ring, generalizing the concept of a Lie triple derivation, and considered the question of when all multiplicative lie n-divergences of a triangular ring T have the so-called standard form.

66 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that every Lie triple derivation on is of the form, where is a derivation of, is a singular Jordan derivation, and is a linear mapping from to its centre that vanishes on.
Abstract: Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.

51 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, it was shown that every Jordan derivation of triangular algebras is a derivation, which is the same as the derivation in the present paper.

90 citations

Journal ArticleDOI
TL;DR: In this paper, the concept of extremal biderivation of a triangular algebra is defined, and it is shown that under certain conditions, under certain assumptions, the extremal and inner biderivities of a triangle algebra can be combined.

81 citations

Journal ArticleDOI
TL;DR: In this article, the authors give a description of Lie derivations of generalized matrix algebras and show how to obtain a Lie derivation of a generalized matrix algebra from a full matrix algebra.

71 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that each biderivation of the Schr dinger-Virasoro Lie algebra over the complex field ℂ is inner and every linear commuting map ψ on 𝔏 has the form ψ(x) ǫ = Ω(x), where Ω is a basis of the one-dimensional center of the center.
Abstract: Let 𝔏 be the Schr dinger–Virasoro Lie algebra over the complex field ℂ. In this article, we prove that each biderivation of 𝔏 is inner. As an application of biderivations, we show that every linear commuting map ψ on 𝔏 has the form ψ(x) = λx + f(x)M 0, where λ ∈ ℂ, M 0 is a basis of the one-dimensional center of 𝔏, and f is a linear function from 𝔏 to ℂ.

69 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that every nonlinear Lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero.

68 citations